Finite Group Databasebeta

← C2×C5×#15691749 #44540237

Subgroups — C2×C5×#15691749 #44540237

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#15691749C211yesmaximal, characteristic, direct product factor, Hall
2C2×C5×C7×C151C311yesmaximal, characteristic, complemented, Hall
3C2×#15691749C511yesmaximal, characteristic, direct product factor, Hall
4C5×C7×C151C2×C311yescharacteristic, complemented, Hall
5C2×C5×C151⋊C3—71nomaximal, Hall
6#15691749C2×C511yescharacteristic, direct product factor, Hall
7C5×C151⋊C3—71noHall
8C2×C7×C151C3×C511yescharacteristic, complemented, Hall
9C2×C5×C151ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
10C7×C151C2×C3×C511yescharacteristic, complemented, Hall
11C2×C151⋊C3—71noHall
12C5×C151C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
13C151⋊C3—71noHall
14C2×C151C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
15C2×C5×ΓL(1,𝔽8)—1511nomaximal, Hall
16C151C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
17C5×ΓL(1,𝔽8)—1511noHall
18C2×C5×C7C151⋊C311yescharacteristic, complemented, Hall
19C2×ΓL(1,𝔽8)—1511noHall
20C5×C7C2×C151⋊C311yescharacteristic, complemented, Hall
21C2×C3×C5—10571noHall
22ΓL(1,𝔽8)—1511noHall
23C3×C5—10571noHall
24C2×C7C5×C151⋊C311yescharacteristic, complemented, Hall
25C2×C5#1569174911yescharacteristic, direct product factor, Hall
26C7C2×C5×C151⋊C311yescharacteristic, complemented, Sylow
27C2×C3—10571noHall
28C5C2×#1569174911yescharacteristic, direct product factor, Sylow
29C3—10571noSylow
30C2C5×#1569174911yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C5#15691749
commutator, cosocle, hypocenterC7×C151C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C151C3
LCSG ▷ C7×C151
UCSC1 ◁ C2×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×#15691749C2direct (N × H)
2. C2×C5×C7×C151C3semidirect
3. C2×#15691749C5direct (N × H)
4. C5×C7×C151C2×C3semidirect
6. #15691749C2×C5direct (N × H)
8. C2×C7×C151C3×C5semidirect
9. C2×C5×C151ΓL(1,𝔽8)semidirect
10. C7×C151C2×C3×C5semidirect
12. C5×C151C2×ΓL(1,𝔽8)semidirect
14. C2×C151C5×ΓL(1,𝔽8)semidirect
16. C151C2×C5×ΓL(1,𝔽8)semidirect
18. C2×C5×C7C151⋊C3semidirect
20. C5×C7C2×C151⋊C3semidirect
24. C2×C7C5×C151⋊C3semidirect
25. C2×C5#15691749direct (N × H)
26. C7C2×C5×C151⋊C3semidirect
28. C5C2×#15691749direct (N × H)
30. C2C5×#15691749direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#156917492
C2×C5×C7×C1513
C2×#156917495
C2×C5×C151⋊C37
C2×C5×ΓL(1,𝔽8)151